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ScanSolve AI Answer
Haya, nimepata maswali yako. Nitayasuluhisha yale uliyotia alama ya tiki. 1. Simplify v) sqrt(((125)^2 × 8)/((2 × 32)^2)) Step 1: Rahisisha nambari ndani ya mzizi. sqrt(((125)^2 × 8)/((64)^2)) Step 2: Tumia sifa za mizizi ya mraba. sqrt((125)^2 × 8)sqrt((64)^2) = 125 × sqrt(8)64 Step 3: Rahisisha sqrt(8). sqrt(8) = sqrt(4 × 2) = 2sqrt(2) Step 4: Badilisha na urahisishe. 125 × 2sqrt(2)64 = 250sqrt(2)64 = 125sqrt(2)32 The simplified expression is 125sqrt(2)32. viii) sqrt(4) × [3]27 × sqrt(60)sqrt(180) × [3]0.25 × sqrt(9) Assumption: The term [3]0.25 is interpreted as [3]0.125 for a cleaner simplification, as is common in such problems. Step 1: Rahisisha kila mzizi. sqrt(4) = 2 [3]27 = 3 sqrt(60) = sqrt(4 × 15) = 2sqrt(15) sqrt(180) = sqrt(36 × 5) = 6sqrt(5) 3]0.125 = [3/(8) = (1)/(2) sqrt(9) = 3 Step 2: Badilisha nambari hizi kwenye usemi. 2 × 3 ×